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Chapter 5: Problem 128

Describe one advantage of expressing a number in scientific notation over decimal notation.

Short Answer

Expert verified
An advantage of expressing a number in scientific notation over decimal notation is that it provides a concise and accurate method for dealing with very large or very small numbers, reducing the risk of errors and making calculations easier.

Step by step solution

01

Understand decimal and scientific notation

Decimal notation is the standard system of writing or representing numbers using base 10. It is composed of a decimal fraction and an integer part. For instance, 3004.75 is in decimal notation. \n\nScientific notation, on the other hand, is a way of expressing numbers that can be quite large or small. It is typically used in scientific calculations where the analysis may require significant digits. It is represented in the form of \(a \times 10^n\), where \(1 \leq a < 10\) and \(n\) is an integer. An example of a number in scientific notation is \(3.00475 \times 10^3\).
02

Identify the advantage of scientific notation

There are numerous advantages of using scientific notation over decimal notation. One clear advantage is that scientific notation allows for the concise and accurate representation of very large or very small numbers. This makes calculations easier and reduces the risk of errors due to mistyping or misreading these numbers. In contrast, decimal notation can become unwieldy and prone to errors when dealing with extremely high or low values.

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